ODE
\[ x^2 y''(x)+5 x y'(x)+13 y(x)=0 \] ODE Classification
[[_Emden, _Fowler]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.169533 (sec), leaf count = 26
\[\left \{\left \{y(x)\to \frac {c_2 \cos (3 \log (x))+c_1 \sin (3 \log (x))}{x^2}\right \}\right \}\]
Maple ✓
cpu = 0.009 (sec), leaf count = 25
\[\left [y \left (x \right ) = \frac {\textit {\_C1} \sin \left (3 \ln \left (x \right )\right )}{x^{2}}+\frac {\textit {\_C2} \cos \left (3 \ln \left (x \right )\right )}{x^{2}}\right ]\] Mathematica raw input
DSolve[13*y[x] + 5*x*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (C[2]*Cos[3*Log[x]] + C[1]*Sin[3*Log[x]])/x^2}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+5*x*diff(y(x),x)+13*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1/x^2*sin(3*ln(x))+_C2/x^2*cos(3*ln(x))]